#### THE

WESTERN INSTITUTE

FOR

ADVANCED STUDY

## GRAND CHALLENGES

We issue Grand Challenges in the fields of mathematics, physics, and biology - or at the intersection of these sciences - then put together a dedicated team of fellows who are highly motivated and well-equipped to pursue the research question. The results undergo a full peer-review process and then are made available to the public.

###### PREVIOUS AND ONGOING GRAND CHALLENGES

First Grand Challenge: The physical basis of consciousness

A mechanistic explanation of consciousness has long been elusive to scientists and philosophers. It is simply not understood what perceptual experience is, how cognitive constructs grow over time, and how we might be able to achieve volitional behavior. The goal of this Grand Challenge was to devise a theoretical framework for understanding consciousness in accordance with physical laws, as a natural emergent property of neural computation. This effort successfully generated a theory that explains these three phenomena, by combining the laws of neuroscience and computational physics. Now we are testing the predictions of this theory in computational simulations, in neuroscience laboratories, and in the clinic.

Ongoing: Tackling computational complexity

The complexity of computational problems can be classified by the time resources required to identify a solution. Computational problems which can be solved in polynomial time by a deterministic Turing machine are classed as P. By contrast, NP problems can be verified in polynomial time but cannot be solved in polynomial time with deterministic computing methods. NP-hard problems include decision problems, search problems, and optimization problems which can be reduced in polynomial time from L to H, where H is a harder computation than L. NP-complete problems are problems which are both NP and NP-hard. The outstanding question is whether problems in this computational complexity class can be practically solved with non-deterministic computing methods. This effort aims to devise operational laws and algebras which guide non-deterministic computing at ambient temperatures.

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Ongoing: Living in an information-filled world

Entropy is both the amount of energy unavailable to do work in a thermodynamic system and a mathematical description of the possible arrangements of particles in that system. A similar equation measures information, the possible arrangements of a system or non-compressibility of a dataset. At the microscopic level, information is the distribution of component pure states in a quantum system. Yet a functional link between these laws has remained out of reach, despite the common element of probabilistic mechanics which provides the foundation for thermodynamics, predictive computation, and quantum theory. This Grand Challenge addresses the following questions: How are information and entropy related? Do they play any significant role in the structure and operation of our universe? What are the implications of living in a probabilistic world, which generates information and entropy?

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Ongoing: The emergent structure of the universe

A long-standing challenge in physics is reconciling quantum mechanics and general relativity. At quantum scales, a fundamental uncertainty in the position and momentum of a particle renders difficulty in measuring the curvature of space-time at its exact location. Meanwhile, at cosmological scales, the curvature of space-time appears irregular and dynamic. The goal of this Grand Challenge is to devise a theoretical framework that describes the curvature of the universe using mechanical laws, rather than empirically-derived constants which are not valid at every scale - with a metric tensor that emerges directly from an extended model of particle physics.